Exact momentum-space analysis of small spin-1/2 $J_1$-$J_2$ rings
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915997192028160 |
|---|---|
| author | Li, Zimeng Wu, Ning |
| author_facet | Li, Zimeng Wu, Ning |
| contents | This paper considers an $N$-site spin-1/2 $J_1$-$J_2$ ring with $N=6$ and $8$. With the help of a set of exact few-magnon Bloch states, we obtain the block-diagonalized Hamiltonian consisting of block matrices of at most four dimensions. Partial of the eigenstates are analytically solved. For the six-site anisotropic ring, we reveal a subset of eigenstates that are simultaneous eigenstates of the Hamiltonian and the total angular momentum operator, even though the latter is not conserved. For both the six- and eight-site isotropic rings, we achieve momentum-space manifestations of several important states, including the famous Majumdar-Ghosh (MG) ground states and the Hamada-Kane-Nakagawa-Natsume (HKNN) ground state. The equivalence of these states with their real-space counterparts is explicitly shown for $N=6$. The structure of the HKNN ground state for small rings suggests that for any even number $N$ this state might behave like a ``bound state" with $N/2$ successive down spins binding together. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_23149 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Exact momentum-space analysis of small spin-1/2 $J_1$-$J_2$ rings Li, Zimeng Wu, Ning Strongly Correlated Electrons This paper considers an $N$-site spin-1/2 $J_1$-$J_2$ ring with $N=6$ and $8$. With the help of a set of exact few-magnon Bloch states, we obtain the block-diagonalized Hamiltonian consisting of block matrices of at most four dimensions. Partial of the eigenstates are analytically solved. For the six-site anisotropic ring, we reveal a subset of eigenstates that are simultaneous eigenstates of the Hamiltonian and the total angular momentum operator, even though the latter is not conserved. For both the six- and eight-site isotropic rings, we achieve momentum-space manifestations of several important states, including the famous Majumdar-Ghosh (MG) ground states and the Hamada-Kane-Nakagawa-Natsume (HKNN) ground state. The equivalence of these states with their real-space counterparts is explicitly shown for $N=6$. The structure of the HKNN ground state for small rings suggests that for any even number $N$ this state might behave like a ``bound state" with $N/2$ successive down spins binding together. |
| title | Exact momentum-space analysis of small spin-1/2 $J_1$-$J_2$ rings |
| topic | Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2604.23149 |